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Licensed Unlicensed Requires Authentication Published by De Gruyter October 13, 2015

Fair compensation for gate and wind conditions in ski jumping – estimated from competition data using a mixed model

  • Magne Aldrin EMAIL logo


Ski jumping is a Winter Olympic sport where the athletes try to fly as far as possible with the best possible style on a ski jumping hill. The best athletes may achieve distances around 100 m on the smallest hills and up to 251.5 m (the world record) on a flying hill. The length of a ski jump is affected by the gate from which the jumpers start, where higher gates give higher speed and therefore longer jumps. Wind conditions are also important, head winds tend to give longer jumps and tail winds tend to give shorter jumps. To ensure relatively fair conditions during competitions, a system including gate and wind compensations was introduced from January 2010. If the conditions change considerably during a round, the jury can change the gate number to avoid too long or too short jumps, and the athlete is then given a compensation (positive or negative). Furthermore, the athletes are given a compensation for the wind conditions during their jump. In this paper, the fairness of this compensation system is investigated by an analysis of the results from 80 ski jumping competitions for men arranged in the World Cup, World Championships and Olympics in the 2011/2012, 2012/2013 and 2013/2014 seasons. The analysis is based on a mixed model. I found that the present compensation for gate number is reasonably fair, but with a tendency for 10% over-compensation. On the other hand, I estimate that the present compensation factor for head winds should be increased by 48% (95% CI 40–57%) and for tail winds by 22% (95% CI 16–30%) to fully compensate for wind conditions.

Corresponding author: Magne Aldrin, Norwegian Computing Center, P.O. Box 114 Blindern, Oslo 0314, Norway; and University of Oslo – Department of Mathematics, P.O. Box 1053 Blindern, Oslo 0317, Norway, e-mail:


I thank Peder Andreas Jansen for valuable comments to drafts of this article.


Akaike, H. 1974. “A New Look at the Statistical Model Identification.” IEEE Transactions on Automatic Control 19:716–723.10.1109/TAC.1974.1100705Search in Google Scholar

Bates, D., M. Maechler, B. Bolker, and S. Walker. 2015a. “Fitting Linear Mixed-effects Models Using lme4.” Journal of Statistical Software, accepted for publication, arXiv:1406.5823 ( in Google Scholar

Bates, D., M. Maechler, B. Bolker, and S. Walker. 2015b. lme4: Linear Mixed-effects Models Using Eigen and S4. R Package Version 1.1-9 ( in Google Scholar

Claeskens, G. and N. Hjort. 2008. Model Selection and Model Averaging. Cambridge: Cambridge University Press.Search in Google Scholar

Efron, B. and R. J. Tibshirani. 1997. An Introduction to the Bootstrap. New York: Chapman and Hall. 450 pp.Search in Google Scholar

FIS. 2014. Home Page of the International Ski Federation (FIS),Oberhofen/Thunersee,Switzerland. Retrieved April 2014 ( in Google Scholar

Pawitan, Y. 2001. In All Likelihood – Statistical Modelling and Inference using Likelihood. Oxford, UK: Clarendon Press.Search in Google Scholar

R Development Core Team. 2009. R: a Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0 ( in Google Scholar

Schwarz, G. 1978. “Estimating the Dimension of a Model.” The Annals of Statistics 6:461–464.10.1214/aos/1176344136Search in Google Scholar

Virmavirta, M. and J. Kivekäs. 2012. “The Effect of Wind on Jumping Distance in Ski Jumping–Fairness Assessed.” Sports Biomechanics 11:358–369.10.1080/14763141.2011.637119Search in Google Scholar PubMed

Zuur, A., E. Ieno, N. Walker, A. Saveliev, and G. Smith. 2009. Mixed Effects Models and Extensions in Ecology with R. 1st ed. New York: Springer, 574 p., doi: 10.1007/978-0-387-87458-6.10.1007/978-0-387-87458-6Search in Google Scholar

Supplemental Material

The online version of this article (DOI: 10.1515/jqas-2015-0022) offers supplementary material, available to authorized users.

Published Online: 2015-10-13
Published in Print: 2015-12-1

©2015 by De Gruyter

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